Bracket polynomial - Revision history

en>Mabulak: added some

2014-05-07T16:44:04Z

added some <math>

← Older revision		Revision as of 18:44, 7 May 2014
Line 1:		Line 1:
	~~An important issue for the [[aeronautics\|aeronautical]] industry is the reduction of [[aircraft noise]].~~ The ~~'''[[rotor (engine)\|rotor]]–[[stator]] interaction'''~~ is ~~a predominant part of~~ the ~~noise emission.~~		The writer is recognized by the title of Figures Lint. For years he's been residing in North Dakota and his family enjoys it. One of the extremely very best things in the world for me is to do aerobics and now I'm trying to make cash with it. Managing people is what I do and the wage has been really fulfilling.<br><br>Feel free to surf to my web site at home std testing ([http://www.animecontent.com/blog/349119 navigate to these guys])
	We will present an introduction to these interaction theory, whose applications are numerous. For example, the conception of air-conditioning ventilators requires a full understanding of this interaction.

	~~==Noise emission of a rotor–stator mechanism==~~
	~~A rotor wake induces on the downstream stator blades a fluctuating vane loading, which is directly linked to the noise emission.~~

	~~We consider a B blades rotor (at a rotation speed of <math>\Omega</math>) and a V blades stator, in a unique rotor–stator configuration. The source frequencies are multiples~~ of ~~<math>B \Omega</math>, that is to say <math>mB \Omega</math>~~. For the moment we don’t have access to the source levels <math>F_{m}</math>. The noise frequencies are also <math>mB \Omega</math>, not depending on the number of blades of the stator. Nevertheless, this number V has a predominant role in ~~the noise levels (<math>P_{m}</math>)~~ and ~~directivity, as~~ it ~~will be discussed later~~.

	~~''Example''~~

	~~''For an airplane air-conditioning ventilator, reasonable data are :''~~

	~~''<math>B=13</math> and <math>\Omega = 12000</math> rnd/min''~~

	~~''The blade passing frequency is 2600 Hz, so we only have to include the first two multiples (2600 Hz and 5200 Hz), because~~ of the ~~human ear high-sensibility limit. We have to study~~ the ~~frequencies m=1 and m=2.''~~

	~~==Optimization of the number of blades==~~
	~~As the source levels can't be easily modified, we have~~ to ~~focus on the interaction between those levels~~ and ~~the noise levels.~~

	~~The transfer function <math>{{F_m } \over {P_m }}</math> contains the following part :~~

	~~<center><math>~~
	~~\sum\limits_{s = - \infty }^{s = + \infty } {e^{ - {{i(mB - sV)\pi } \over 2}} J_{mB - sV} } (mBM)~~
	~~</math></center>~~

	~~Where '~~'m'' is the [[Mach number]] and <math>J_{mB - sV}</math> the [[Bessel function]] of ''mB''–''sV'' order. In order to minimize the influence of the transfer function, the goal is to reduce the value of this Bessel function. To do so, the argument must be smaller than the order of the Bessel function.

	~~''Back~~ to ~~the example :''~~

	~~''For m=1,~~ with ~~a Mach number M=0~~.~~3, the argument of the Bessel function~~ is ~~about 4. We have to avoid having mB-sV inferior than 4. If V=10, we have 13-1x10=3, so there will be a noisy mode. If V=19, the minimum of mB-sV is 6,~~ and the ~~noise emission will be limited.''~~

	~~''Remark :''~~

	~~''The case that is to be strictly avoided is when mB-sV can be nul, which causes the order of the Bessel function to be 0. As a consequence, we have to take care having B and V prime numbers.''~~

	~~==Determination of source levels==~~
	~~The minimization of the transfer function <math>{{F_m } \over {P_m }}</math> is a great step in the process of reducing the noise emission~~. ~~Nevertheless, to be highly efficient, we also have to predict the source levels~~ <~~math~~>~~F_{m}~~<~~/math~~>~~. This will lead us~~ to ~~choose~~ to ~~minimize the Bessel functions for the most significant values of m. For example, if the source level for m=1 is very higher than for m=2, we will not consider the Bessel functions of order 2B-sV.~~
	~~The determination of the source levels is given by the Sears theory,which will not be explicated here.~~

	~~==Directivity==~~
	All this study was made for a privileged direction : the axis of the rotor–stator. All the results are acceptable when the noise reduction is ought to be in this direction. In the case where the noise to reduce is perpendicular to the axis, the results are very different, as those figures shown :

	~~For B=13 and V=13, which is the worst case, we see that the sound level is very high on the axis~~ (~~for <math>\theta = 0</math>)~~

	~~For B=13 and V=19, the sound level is very low on the axis but high perpendicularly to the axis (for <math>\theta = Pi/2</math>)~~

	~~<center>~~[~~[File:Acoustics 1319.jpg]]</center>~~

	~~==External links==~~
	* {{cite web \| url=http://www.~~nlr~~.nl/~~smartsite.dws?id=2863 \| publisher=[[National Aerospace Laboratory~~]], [[Netherlands]] \| first1=P. \| last1=Sijtsma \| first2=J.B.H.M. \| last2=Schulten \| year=2003 \| title=Wake modelling accuracy requirements for prediction of rotor wake-stator interaction noise (NLR-TP-2003-124; AIAA Paper 2003-3138) ~~\| accessdate=9 March 2009 }}~~

	~~{{DEFAULTSORT:Rotor-stator interaction}}~~
	~~[[Category:Aerodynamics]]~~

en>Hyacinth: {{Knot theory}}

2013-05-22T09:13:45Z

← Older revision		Revision as of 11:13, 22 May 2013
Line 1:		Line 1:
	~~They contact me Emilia~~. ~~One~~ of the ~~things she loves most~~ is to ~~do aerobics~~ and ~~now she~~ is ~~trying~~ to ~~earn cash with~~ it. ~~North Dakota~~ is ~~her beginning place but she will~~ have to ~~move~~ 1 ~~working day or another~~. For ~~years I~~'~~ve been operating as~~ a ~~payroll clerk~~.<br><br>~~my site~~: ~~at home std testing~~ ([http://www.~~kindrasdesigns-testing~~.~~com~~/~~index~~.~~php~~?do=~~/profile~~-~~12578/info/ mouse click the following post~~])		An important issue for the [[aeronautics\|aeronautical]] industry is the reduction of [[aircraft noise]]. The '''[[rotor (engine)\|rotor]]–[[stator]] interaction''' is a predominant part of the noise emission.
			We will present an introduction to these interaction theory, whose applications are numerous. For example, the conception of air-conditioning ventilators requires a full understanding of this interaction.

			==Noise emission of a rotor–stator mechanism==
			A rotor wake induces on the downstream stator blades a fluctuating vane loading, which is directly linked to the noise emission.

			We consider a B blades rotor (at a rotation speed of <math>\Omega</math>) and a V blades stator, in a unique rotor–stator configuration. The source frequencies are multiples of <math>B \Omega</math>, that is to say <math>mB \Omega</math>. For the moment we don’t have access to the source levels <math>F_{m}</math>. The noise frequencies are also <math>mB \Omega</math>, not depending on the number of blades of the stator. Nevertheless, this number V has a predominant role in the noise levels (<math>P_{m}</math>) and directivity, as it will be discussed later.

			''Example''

			''For an airplane air-conditioning ventilator, reasonable data are :''

			''<math>B=13</math> and <math>\Omega = 12000</math> rnd/min''

			''The blade passing frequency is 2600 Hz, so we only have to include the first two multiples (2600 Hz and 5200 Hz), because of the human ear high-sensibility limit. We have to study the frequencies m=1 and m=2.''

			==Optimization of the number of blades==
			As the source levels can't be easily modified, we have to focus on the interaction between those levels and the noise levels.

			The transfer function <math>{{F_m } \over {P_m }}</math> contains the following part :

			<center><math>
			\sum\limits_{s = - \infty }^{s = + \infty } {e^{ - {{i(mB - sV)\pi } \over 2}} J_{mB - sV} } (mBM)
			</math></center>

			Where ''m'' is the [[Mach number]] and <math>J_{mB - sV}</math> the [[Bessel function]] of ''mB''–''sV'' order. In order to minimize the influence of the transfer function, the goal is to reduce the value of this Bessel function. To do so, the argument must be smaller than the order of the Bessel function.

			''Back to the example :''

			''For m=1, with a Mach number M=0.3, the argument of the Bessel function is about 4. We have to avoid having mB-sV inferior than 4. If V=10, we have 13-1x10=3, so there will be a noisy mode. If V=19, the minimum of mB-sV is 6, and the noise emission will be limited.''

			''Remark :''

			''The case that is to be strictly avoided is when mB-sV can be nul, which causes the order of the Bessel function to be 0. As a consequence, we have to take care having B and V prime numbers.''

			==Determination of source levels==
			The minimization of the transfer function <math>{{F_m } \over {P_m }}</math> is a great step in the process of reducing the noise emission. Nevertheless, to be highly efficient, we also have to predict the source levels <math>F_{m}</math>. This will lead us to choose to minimize the Bessel functions for the most significant values of m. For example, if the source level for m=1 is very higher than for m=2, we will not consider the Bessel functions of order 2B-sV.
			The determination of the source levels is given by the Sears theory,which will not be explicated here.

			==Directivity==
			All this study was made for a privileged direction : the axis of the rotor–stator. All the results are acceptable when the noise reduction is ought to be in this direction. In the case where the noise to reduce is perpendicular to the axis, the results are very different, as those figures shown :

			For B=13 and V=13, which is the worst case, we see that the sound level is very high on the axis (for <math>\theta = 0</math>)

			For B=13 and V=19, the sound level is very low on the axis but high perpendicularly to the axis (for <math>\theta = Pi/2</math>)

			<center>[[File:Acoustics 1319.jpg]]</center>

			==External links==
			* {{cite web \| url=http://www.nlr.nl/smartsite.dws?id=2863 \| publisher=[[National Aerospace Laboratory]], [[Netherlands]] \| first1=P. \| last1=Sijtsma \| first2=J.B.H.M. \| last2=Schulten \| year=2003 \| title=Wake modelling accuracy requirements for prediction of rotor wake-stator interaction noise (NLR-TP-2003-124; AIAA Paper 2003-3138) \| accessdate=9 March 2009 }}

			{{DEFAULTSORT:Rotor-stator interaction}}
			[[Category:Aerodynamics]]

128.131.208.200: polynomial with variable A

2012-06-01T10:49:02Z

polynomial with variable A

New page

They contact me Emilia. One of the things she loves most is to do aerobics and now she is trying to earn cash with it. North Dakota is her beginning place but she will have to move 1 working day or another. For years I've been operating as a payroll clerk.<br><br>my site: at home std testing ([http://www.kindrasdesigns-testing.com/index.php?do=/profile-12578/info/ mouse click the following post])